Solve 21/3-51/9-34/27=

$$2 \frac { 1 } { 3 } - 5 \frac { 1 } { 9 } - 3 \frac { 4 } { 27 } =$$

Evaluate

$$-\frac{160}{27}\approx -5.925925926$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{6+1}{3}-\frac{5\times 9+1}{9}-\frac{3\times 27+4}{27}$$

Add 6 and 1 to get 7.

$$\frac{7}{3}-\frac{5\times 9+1}{9}-\frac{3\times 27+4}{27}$$

Multiply 5 and 9 to get 45.

$$\frac{7}{3}-\frac{45+1}{9}-\frac{3\times 27+4}{27}$$

Add 45 and 1 to get 46.

$$\frac{7}{3}-\frac{46}{9}-\frac{3\times 27+4}{27}$$

Least common multiple of 3 and 9 is 9. Convert \frac{7}{3} and \frac{46}{9} to fractions with denominator 9.

$$\frac{21}{9}-\frac{46}{9}-\frac{3\times 27+4}{27}$$

Since \frac{21}{9} and \frac{46}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21-46}{9}-\frac{3\times 27+4}{27}$$

Subtract 46 from 21 to get -25.

$$-\frac{25}{9}-\frac{3\times 27+4}{27}$$

Multiply 3 and 27 to get 81.

$$-\frac{25}{9}-\frac{81+4}{27}$$

Add 81 and 4 to get 85.

$$-\frac{25}{9}-\frac{85}{27}$$

Least common multiple of 9 and 27 is 27. Convert -\frac{25}{9} and \frac{85}{27} to fractions with denominator 27.

$$-\frac{75}{27}-\frac{85}{27}$$

Since -\frac{75}{27} and \frac{85}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-75-85}{27}$$

Subtract 85 from -75 to get -160.

$$-\frac{160}{27}$$

Factor

$$-\frac{160}{27} = -5\frac{25}{27} = -5.925925925925926$$